83 citations · 130 across the 28 of their papers we have counts for
30 papers
A Unified Framework for Randomized Row-Action Methods for Structured Data Fitting and Constraint Geometry
Valentin Leplat, Zeyu Dong, Junfeng Yin
We study randomized row-action methods for problems with linear observations, convex constraints, and non-Euclidean geometry. Our starting point is a unified formulation in which t…
Iterative Methods for Computing the Moore--Penrose Inverse of Split-Quaternion Matrices with Applications
Salman Ahmadi-Asl, Valentin Leplat, Mohammad S. Alkousa
We study iterative methods for computing the Moore--Penrose inverse of split-quaternion matrices. We first establish a consistent framework based on a \(2\times2\) real representat…
Quaternion Maximum-Volume Submatrix Selection with Applications to Multichannel Imaging and Visual Data
Vsevolod Kliushev, Junjun Pan, Valentin Leplat
Low-rank approximation based on selected rows and columns is a useful alternative to singular value decompositions when the goal is an interpretable and compact matrix representati…
Adaptive Randomized Pivoting for Tensor Cross Approximation in the T-Product Framework
Ahmadsho Akdodshoev, Valentin Leplat, Salman Ahmadi-Asl
This paper studies extensions of adaptive randomized pivoting (ARP), recently introduced for matrix column subset selection, to tensors in the t-product framework. We propose two c…
Prox-NAG-GS: A Semi-Implicit Proximal Method for Composite Optimization
Sikeh Gisele Wiykiynyuy, Kelvin Asu Ekuri, Valentin Leplat
Composite optimization problems, where a smooth loss is combined with a nonsmooth regularizer, are common in machine learning and inverse problems. In this work, we study a proxima…
IRON: Implicit Resolvent Optimization under Noise
Valentin Leplat, Roland Hildebrand
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gr…
QuatIca: Advanced Numerical Linear Algebra and Optimization for Quaternionic Matrices in Python
Valentin Leplat, Salman Ahmadi-Asl, Junjun Pan +2
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time seri…
A New Tensor Network: Tubal Tensor Train and Its Applications
Salman Ahmadi-Asl, Valentin Leplat, Anh-Huy Phan +1
We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-…
Joint Majorization-Minimization for Nonnegative CP and Tucker Decompositions under -Divergences: Unfolding-Free Updates
Valentin Leplat
We study majorization-minimization methods for nonnegative tensor decompositions under the -divergence family, focusing on nonnegative CP and Tucker models. Our aim is to avoid…
A Provably-Correct and Robust Convex Model for Smooth Separable NMF
Junjun Pan, Valentin Leplat, Michael Ng +1
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF…
Market-Driven Subset Selection for Budgeted Training
Ashish Jha, Valentin Leplat, AH Phan
Training large language models on massive datasets is computationally expensive, yet empirical evidence suggests that substantial portions of training examples contribute minimally…
GRAFT: Gradient-Aware Fast MaxVol Technique for Dynamic Data Sampling
Ashish Jha, Anh huy Phan, Razan Dibo +1
Training modern neural networks on large datasets is computationally and environmentally costly. We introduce GRAFT, a scalable in-training subset selection method that (i) extract…
Constrained Optimization via Constraint-Induced Geometry: Implicit Feasible Dynamics and Optimality from Stationarity
Valentin Leplat
We introduce Gravidy, a geometry-aware framework for constrained optimization in which constraints are encoded directly into the dynamics, so the motion remains feasible by constru…
Norm-Constrained Flows and Sign-Based Optimization: Theory and Algorithms
Valentin Leplat, Sergio Mayorga, Roland Hildebrand +1
Sign Gradient Descent (SignGD) uses only the coordinate-wise sign of the gradient. We study this method through norm-constrained continuous-time dynamics: at each point, the veloci…
Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications
Valentin Leplat, Salman Ahmadi-Asl, JunJun Pan +1
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a da…
Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices
Salman Ahmadi-Asl, Malihe Nobakht Kooshkghazi, Valentin Leplat
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ab…
Nonnegative Tensor Decomposition Via Collaborative Neurodynamic Optimization
Salman Ahmadi-Asl, Valentin Leplat, Anh-Huy Phan +1
This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural ne…
Ruppert-Polyak averaging for Stochastic Order Oracle
V. N. Smirnov, K. M. Kazistova, I. A. Sudakov +3
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this i…
An Alternating Minimization Algorithm with Trajectory for Direct Exoplanet Detection -- The AMAT Algorithm
Hazan Daglayan, Simon Vary, Olivier Absil +6
Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard PSF subtraction methods use techniques based on a low-rank approximat…
Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models
Jeremy E. Cohen, Valentin Leplat
Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensional…
Block Majorization Minimization with Extrapolation and Application to -NMF
Le Thi Khanh Hien, Valentin Leplat, Nicolas Gillis
We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are up…
Deep Nonnegative Matrix Factorization with Beta Divergences
Valentin Leplat, Le Thi Khanh Hien, Akwum Onwunta +1
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all exist…
Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation
Hazan Daglayan, Simon Vary, Valentin Leplat +2
We propose to use low-rank matrix approximation using the component-wise L1-norm for direct imaging of exoplanets. Exoplanet detection by direct imaging is a challenging task for t…
NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer
Valentin Leplat, Daniil Merkulov, Aleksandr Katrutsa +3
Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted…